Geodesic
$L^p$ estimates for degenerate elliptic systems with VMO coefficients
Algebra i analiz, Tome 25 (2013) no. 6, pp. 24-36.

Voir la notice de l'article provenant de la source Math-Net.Ru

Interior $L^p$ gradient weighted estimates are proved for degenerate elliptic systems in divergence form with VMO coefficients.
Keywords: Muckenhoupt weights, degenerate elliptic systems, VMO. 
@article{AA_2013_25_6_a1,
     author = {G. di Fazio and M. S. Fanciullo and P. Zamboni},
     title = {$L^p$ estimates for degenerate elliptic systems with {VMO} coefficients},
     journal = {Algebra i analiz},
     pages = {24--36},
     publisher = {mathdoc},
     volume = {25},
     number = {6},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2013_25_6_a1/}
}
TY  - JOUR
AU  - G. di Fazio
AU  - M. S. Fanciullo
AU  - P. Zamboni
TI  - $L^p$ estimates for degenerate elliptic systems with VMO coefficients
JO  - Algebra i analiz
PY  - 2013
SP  - 24
EP  - 36
VL  - 25
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2013_25_6_a1/
LA  - en
ID  - AA_2013_25_6_a1
ER  - 
%0 Journal Article
%A G. di Fazio
%A M. S. Fanciullo
%A P. Zamboni
%T $L^p$ estimates for degenerate elliptic systems with VMO coefficients
%J Algebra i analiz
%D 2013
%P 24-36
%V 25
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2013_25_6_a1/
%G en
%F AA_2013_25_6_a1
G. di Fazio; M. S. Fanciullo; P. Zamboni. $L^p$ estimates for degenerate elliptic systems with VMO coefficients. Algebra i analiz, Tome 25 (2013) no. 6, pp. 24-36. http://geodesic.mathdoc.fr/item/AA_2013_25_6_a1/

[1] Agmon S., Douglis A., Nirenberg L., “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I”, Comm. Pure Appl. Math., 12 (1959), 623–727 ; “II”, Comm. Pure Appl. Math., 17 (1964), 35–92 | DOI | MR | Zbl | DOI | MR | Zbl

[2] Bramanti M., Brandolini L., “$L^p$ estimates for nonvariational hypoelliptic operators with VMO coefficients”, Trans. Amer. Math. Soc., 352:2 (2000), 781–822 | DOI | MR | Zbl

[3] Bramanti M., Cerutti M. C., “$W_p^{1,2}$ solvability for the Cauchy–Dirichlet problem for parabolic equations with VMO coefficients”, Comm. Partial Differential Equations, 18:9–10 (1993), 1735–1763 | DOI | MR | Zbl

[4] Bramanti M., Fanciullo M. S., “BMO estimates for nonvariational operators with discontinuous coefficients structured on Hörmander vector fields on Carnot groups”, Ad. in Dif. Equations, 18:9–10 (2013), 955–1004 | MR | Zbl

[5] Byun S., Wang L., “Elliptic equations with BMO nonlinearity in Reifenberg domains”, Adv. Math., 219:6 (2008), 1937–1971 | DOI | MR | Zbl

[6] Campanato S., “Un risultato relativo ad equazioni ellittiche del secondo ordine di tipo non variazionale”, Ann. Scuola Norm. Sup. Pisa (3), 21 (1967), 701–707 | MR | Zbl

[7] Campanato S., Stampacchia G., “Sulle maggiorazioni in $L^p$ nella teoria delle equazioni ellittiche”, Boll. Unione Mat. Ital. (3), 20 (1965), 393–399 | MR | Zbl

[8] Chiarenza F., Franciosi M., “A generalization of a theorem by C. Miranda”, Ann. Mat. Pura Appl. (4), 161 (1992), 285–297 | DOI | MR | Zbl

[9] Chiarenza F., Franciosi M., Frasca M., “$L^p$-estimates for linear elliptic systems with discontinuous coefficients”, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 5:1 (1994), 27–32 | MR | Zbl

[10] Chiarenza F., Frasca M., Longo P., “Interior $W^{2,p}$ estimates for nondivergence elliptic equations with discontinuous coefficients”, Ricerche Mat., 40:1 (1991), 149–168 | MR | Zbl

[11] Chiarenza F., Frasca M., Longo P., “$W^{2,p}$ solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients”, Trans. Amer. Math. Soc., 336:2 (1993), 841–853 | MR | Zbl

[12] Di Fazio G., “$L^p$ estimates for divergence form elliptic equations with discontinuous coefficients”, Boll. Unione Mat. Ital. A (7), 10:2 (1996), 409–420 | MR | Zbl

[13] Di Fazio G., Fanciullo M. S., “Gradient estimates for elliptic systems in Carnot–Carathéodory spaces”, Comment. Math. Univ. Carolin., 43:4 (2002), 605–618 | MR | Zbl

[14] Di Fazio G., Fanciullo M. S., Zamboni P., “Harnack inequality and smoothness for quasilinear degenerate elliptic equations”, J. Differential Equations, 245:10 (2008), 2939–2957 | DOI | MR | Zbl

[15] Di Fazio G., Fanciullo M. S., Zamboni P., “Harnack inequality and regularity for degenerate quasilinear elliptic equations”, Math. Z., 264:3 (2010), 679–695 | DOI | MR | Zbl

[16] Di Fazio G., Fanciullo M. S., Zamboni P., “Harnack inequality for a class of strongly degenerate elliptic operators formed by Hörmander vector fields”, Manuscripta Math., 135:3–4 (2011), 361–380 | DOI | MR | Zbl

[17] Di Fazio G., Fanciullo M. S., Zamboni P., “Interior $L^p$ estimates for degenerate elliptic equations in divergence form with VMO coefficients”, Differential Integral Equations, 25:7–8 (2012), 619–628 | MR | Zbl

[18] Di Fazio G., Fanciullo M. S., Zamboni P., “Hölder regularity for non divergence form elliptic equations with discontinuous coefficients”, J. of Math. Anal. Appl., 407:11 (2013), 545–549 | DOI | MR

[19] Di Fazio G., Fanciullo M. S., Zamboni P., “Regularity for a class of strongly degenerate quasilinear operators”, J. Differential Equations, 255:13 (2013), 3920–3939 | DOI | MR | Zbl

[20] Di Fazio G., Palagachev D. K., Ragusa M. A., “Global Morrey regularity of strong solutions to the Dirichlet problem for elliptic equations with discontinuous coefficients”, J. Funct. Anal., 166:2 (1999), 179–196 | DOI | MR | Zbl

[21] Di Fazio G., Ragusa M. A., “Interior estimates in Morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients”, J. Funct. Anal., 112:2 (1993), 241–256 | DOI | MR | Zbl

[22] Di Fazio G., Zamboni P., “Hölder continuity for quasilinear subelliptic equations in Carnot Caratheodory spaces”, Math. Nachr., 272 (2004), 3–10 | DOI | MR | Zbl

[23] Di Fazio G., Zamboni P., “Local regularity of solutions to quasilinear subelliptic equations in Carnot Caratheodory spaces”, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 9:2 (2006), 485–504 | MR | Zbl

[24] Di Fazio G., Zamboni P., “Regularity for quasilinear degenerate elliptic equations”, Math. Z., 253:4 (2006), 787–803 | DOI | MR | Zbl

[25] Di Fazio G., Zamboni P., “Unique continuation for positive solutions of degenerate elliptic equations”, Math. Nachr., 283:7 (2010), 994–999 | MR | Zbl

[26] Fabes E., Kenig C., Serapioni R., “The local regularity of solutions of degenerate elliptic equations”, Comm. Partial Differential Equations, 7:1 (1982), 77–116 | DOI | MR | Zbl

[27] John F., Nirenberg L., “On functions of bounded mean oscillation”, Comm. Pure Appl. Math., 14 (1961), 415–426 | DOI | MR | Zbl

[28] Kim D., Krylov N. V., “Elliptic differential equations with coefficients measurable with respect to one variable and VMO with respect to the others”, SIAM J. Math. Anal., 39:2 (2007), 489–506 | DOI | MR | Zbl

[29] Krylov N. V., Lectures on elliptic and parabolic equations in Sobolev spaces, Graduate Studies in Math., 96, Amer. Math. Soc., Providence, RI, 2008 | MR | Zbl

[30] Miranda C., “Sulle equazioni ellittiche del secondo ordine di tipo non variazionale a coefficienti discontinui”, Ann. Math. Pura Appl. (4), 63 (1963), 353–386 | DOI | MR | Zbl

[31] Palagachev D. K., “Quasilinear elliptic equations with VMO coefficients”, Trans. Amer. Math. Soc., 347:7 (1995), 2481–2493 | DOI | MR | Zbl

[32] Ragusa M. A., “Local Hölder regularity for solutions of elliptic systems”, Duke Math. J., 113:2 (2002), 385–397 | DOI | MR | Zbl

[33] Sarason D., “Functions of vanishing mean oscillation”, Trans. Amer. Math. Soc., 207 (1975), 391–405 | DOI | MR | Zbl

[34] Vitanza C., Zamboni P., “A variational inequality for a degenerate elliptic operator under minimal assumptions on the coefficients”, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 10:2 (2007), 341–356 | MR | Zbl